%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYN352-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:24:20 EDT 2022
% Result : Unsatisfiable 1.57s 1.77s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 3 unt; 3 nHn; 7 RR)
% Number of literals : 23 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ f(b,z(A,B))
| ~ f(A,z(A,B))
| f(z(A,B),z(A,B)) ),
file('SYN352-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ f(A,B)
| ~ f(A,z(A,B))
| ~ f(B,z(A,B)) ),
file('SYN352-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ f(A,B)
| f(A,z(A,B))
| f(B,z(A,B)) ),
file('SYN352-1.p',unknown),
[] ).
cnf(6,plain,
( ~ f(b,z(b,A))
| f(z(b,A),z(b,A)) ),
inference(factor,[status(thm)],[2]),
[iquote('factor,2.1.2')] ).
cnf(7,plain,
( ~ f(A,A)
| ~ f(A,z(A,A)) ),
inference(factor,[status(thm)],[3]),
[iquote('factor,3.2.3')] ).
cnf(8,plain,
( ~ f(A,A)
| f(A,z(A,A)) ),
inference(factor,[status(thm)],[4]),
[iquote('factor,4.2.3')] ).
cnf(11,axiom,
( f(b,z(A,B))
| f(A,z(A,B))
| f(z(A,B),z(A,B)) ),
file('SYN352-1.p',unknown),
[] ).
cnf(12,plain,
( f(b,z(b,A))
| f(z(b,A),z(b,A)) ),
inference(factor,[status(thm)],[11]),
[iquote('factor,11.1.2')] ).
cnf(32,plain,
f(z(b,A),z(b,A)),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[12,6])]),
[iquote('hyper,12,6,factor_simp')] ).
cnf(47,plain,
f(z(b,A),z(z(b,A),z(b,A))),
inference(hyper,[status(thm)],[32,8]),
[iquote('hyper,32,8')] ).
cnf(49,plain,
$false,
inference(hyper,[status(thm)],[47,7,32]),
[iquote('hyper,47,7,32')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN352-1 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 11:05:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.57/1.77 ----- Otter 3.3f, August 2004 -----
% 1.57/1.77 The process was started by sandbox2 on n004.cluster.edu,
% 1.57/1.77 Wed Jul 27 11:05:36 2022
% 1.57/1.77 The command was "./otter". The process ID is 22208.
% 1.57/1.77
% 1.57/1.77 set(prolog_style_variables).
% 1.57/1.77 set(auto).
% 1.57/1.77 dependent: set(auto1).
% 1.57/1.77 dependent: set(process_input).
% 1.57/1.77 dependent: clear(print_kept).
% 1.57/1.77 dependent: clear(print_new_demod).
% 1.57/1.77 dependent: clear(print_back_demod).
% 1.57/1.77 dependent: clear(print_back_sub).
% 1.57/1.77 dependent: set(control_memory).
% 1.57/1.77 dependent: assign(max_mem, 12000).
% 1.57/1.77 dependent: assign(pick_given_ratio, 4).
% 1.57/1.77 dependent: assign(stats_level, 1).
% 1.57/1.77 dependent: assign(max_seconds, 10800).
% 1.57/1.77 clear(print_given).
% 1.57/1.77
% 1.57/1.77 list(usable).
% 1.57/1.77 0 [] f(a,b).
% 1.57/1.77 0 [] -f(X,Y)|f(b,z(X,Y))|f(Y,z(X,Y)).
% 1.57/1.77 0 [] f(X,Y)|f(z(X,Y),z(X,Y)).
% 1.57/1.77 0 [] f(b,z(X,Y))|f(X,z(X,Y))|f(z(X,Y),z(X,Y)).
% 1.57/1.77 0 [] -f(b,z(X,Y))| -f(X,z(X,Y))|f(z(X,Y),z(X,Y)).
% 1.57/1.77 0 [] -f(X,Y)| -f(X,z(X,Y))| -f(Y,z(X,Y)).
% 1.57/1.77 0 [] -f(X,Y)|f(X,z(X,Y))|f(Y,z(X,Y)).
% 1.57/1.77 end_of_list.
% 1.57/1.77
% 1.57/1.77 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.57/1.77
% 1.57/1.77 This is a non-Horn set without equality. The strategy will
% 1.57/1.77 be ordered hyper_res, unit deletion, and factoring, with
% 1.57/1.77 satellites in sos and with nuclei in usable.
% 1.57/1.77
% 1.57/1.77 dependent: set(hyper_res).
% 1.57/1.77 dependent: set(factor).
% 1.57/1.77 dependent: set(unit_deletion).
% 1.57/1.77
% 1.57/1.77 ------------> process usable:
% 1.57/1.77 ** KEPT (pick-wt=13): 1 [] -f(A,B)|f(b,z(A,B))|f(B,z(A,B)).
% 1.57/1.77 ** KEPT (pick-wt=17): 2 [] -f(b,z(A,B))| -f(A,z(A,B))|f(z(A,B),z(A,B)).
% 1.57/1.77 ** KEPT (pick-wt=13): 3 [] -f(A,B)| -f(A,z(A,B))| -f(B,z(A,B)).
% 1.57/1.77 ** KEPT (pick-wt=13): 4 [] -f(A,B)|f(A,z(A,B))|f(B,z(A,B)).
% 1.57/1.77
% 1.57/1.77 ------------> process sos:
% 1.57/1.77 ** KEPT (pick-wt=3): 9 [] f(a,b).
% 1.57/1.77 ** KEPT (pick-wt=10): 10 [] f(A,B)|f(z(A,B),z(A,B)).
% 1.57/1.77 ** KEPT (pick-wt=17): 11 [] f(b,z(A,B))|f(A,z(A,B))|f(z(A,B),z(A,B)).
% 1.57/1.77
% 1.57/1.77 ======= end of input processing =======
% 1.57/1.77
% 1.57/1.77 =========== start of search ===========
% 1.57/1.77
% 1.57/1.77 -------- PROOF --------
% 1.57/1.77
% 1.57/1.77 -----> EMPTY CLAUSE at 0.01 sec ----> 49 [hyper,47,7,32] $F.
% 1.57/1.77
% 1.57/1.77 Length of proof is 6. Level of proof is 3.
% 1.57/1.77
% 1.57/1.77 ---------------- PROOF ----------------
% 1.57/1.77 % SZS status Unsatisfiable
% 1.57/1.77 % SZS output start Refutation
% See solution above
% 1.57/1.77 ------------ end of proof -------------
% 1.57/1.77
% 1.57/1.77
% 1.57/1.77 Search stopped by max_proofs option.
% 1.57/1.77
% 1.57/1.77
% 1.57/1.77 Search stopped by max_proofs option.
% 1.57/1.77
% 1.57/1.77 ============ end of search ============
% 1.57/1.77
% 1.57/1.77 -------------- statistics -------------
% 1.57/1.77 clauses given 8
% 1.57/1.77 clauses generated 154
% 1.57/1.77 clauses kept 48
% 1.57/1.77 clauses forward subsumed 112
% 1.57/1.77 clauses back subsumed 14
% 1.57/1.77 Kbytes malloced 976
% 1.57/1.77
% 1.57/1.77 ----------- times (seconds) -----------
% 1.57/1.77 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.57/1.77 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.57/1.77 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.57/1.77
% 1.57/1.77 That finishes the proof of the theorem.
% 1.57/1.77
% 1.57/1.77 Process 22208 finished Wed Jul 27 11:05:37 2022
% 1.57/1.77 Otter interrupted
% 1.57/1.77 PROOF FOUND
%------------------------------------------------------------------------------